"Make someone's hair stand on end" refers to a person's feeling of intense fear or shock that causes their hair follicles to become erect, giving a shivering sensation. Antonyms for this phrase would include "calm," "comfort," "soothe," "relax," "assure, "reassure," etc. When someone is "calm," "comforted," "soothed," or "relaxed," they tend to feel at ease or peaceful, free from any tension or anxiety. Similarly, when someone is "assured" or "reassured," they feel more confident or secure, knowing that everything is going to be fine.